Consumer choice

Question 1

What is the consumprion set?

Answer 1

The consumprion set X ⊆ R^L is the subset of the commodity space consisting in the bundles that can acturally be consumed

Question 2

what is the budget constraint?

Answer 2

Σpi * xi ≤ w

Question 3

What is the Walrasian budget set?

Answer 3

B(p, w) = {x ∈ X | p*x ≤ w}

Question 4

What is the Walrasian demand?

Answer 4

It is a correspondence x: P X W ⇉ X such that ∅ ⊂ x(p,w) ⊂ B(p, w) for every (p,w) ∈ P X W

Question 5

What are the two important assumpionts of the Walrasian Demand?

Answer 5

1) Homogeneous of degree zero

2) Walras’ Law

Question 6

What does the aassumption of homogneous of degree zero mean?

Answer 6

x(αp, αw) = x(p,w)

Question 7

What does the assumption of Walras’ Law mean?

Answer 7

For every (p, w) we have p*x =w for all x ∈ x(p,w)

Question 8

What is the Engel effect?

Answer 8

Let price fixed, see the impact of wealth changes in the demand

Question 9

What is the Wealth expansion path?

Answer 9

The graph of how the growth of wealth impacts on the demand if the prices are fixed

Question 10

How the Wealth effect is calculated?

Answer 10

∂xi(p,w) / ∂w

Question 11

If ∂xi(p,w) / ∂w ≥ 0

Answer 11

Good I is normal at (p, w)

Question 12

If ∂xi(p,w) / ∂w ≤ 0

Answer 12

Good I is inferior at (p, w)

Question 13

How the price effect is calulated?

Answer 13

∂xi(p,w) / ∂p

Question 14

If ∂xi(p,w) / ∂p ≥ 0

Answer 14

good I is typical at (p, w)

Question 15

If ∂xi(p,w) / ∂p ≤ 0

Answer 15

Good I is Giffen at (p, w)

Question 16

Dv (v*w) = ?

Answer 16

w^T

Question 17

Dv ||v|| =?

Answer 17

v^T / ||v||

Question 18

Dv(v^T * A) = V^T (A + A^T)

Answer 18

Dv f(V) = ∇f(v)^T

Question 19

Dv v = ?

Answer 19

I

Question 20

Dv (Av) = ?

Answer 20

A

Question 21

Dv (g(f(v)) = ? (Chain Rule)

Answer 21

Dw g(w) * Dv(f(v)

Question 22

Dv [g(v) * f(V)] = ? (Product Rule)

Answer 22

g(v)^T * Df(V) + f(v)^T * Dg(v)

Question 23

If x(p, w) is homogeneous of degree zero then…

Answer 23

Σ ∂xi(p,w)/∂pk *pk + ∂xi(p,w)/∂w =0
Ou 
Dp x(p,w) * p + Dw x(p,w)*w = 0

Question 24

If x(p,w) satisfies the Walras’ Law, then:

Answer 24

Σ∂xi(p,w)/∂pk * pi + xk(p, w) = 0 
e
Σ∂xi(p,w)/∂w = 1
Ou
p*Dp X(p,w) + x(p,w)^T = 0^T
e
p*Dw(p,w) = 1

Question 25

x(p,w) satisfy homeenity of dregree zero and the Walras’ law iff

Answer 25

Dp x(p,w) * p + Dw x(p,w)*w = 0
p*Dp X(p,w) + x(p,w)^T = 0^T
e
p*Dw(p,w) = 1
hold for all (p,w)